Question

sphere of maximum size is carved out of a solid wooden cylinder of diameter 15cm and height 12 cm. what is volume of largest solidsphere that can be carved out

Answer 1

the radius of the sphere will be 6cm
so... volume can be calculated from the formula 4/3πr^3

Answer 2

The volume of largest solid sphere is $\bold{1767.85\ \mathrm{cm}^{3}}$.

Solution:

Given: Solid wooden cylinder of diameter 15cm and height 12 cm.  

Sphere can be defined as a “round solid figure, or its surface, with every point” on its “surface equidistant” from its centre.

$\text {Radius}=\frac{\text {Diameter}}{2}$

$=\frac{15}{2}=7.5\ \mathrm{cm}$  i.e. the radius

Volume of sphere $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times \frac{75}{10} \times \frac{75}{10} \times \frac{75}{10}$

$=11 \times 5 \times 15 \times \frac{15}{7}$

$=\frac{12375}{7}$

$=1767.85\ \mathrm{cm}^{3}$